Matrices: Definitions and Fundamental Operations

Abstract

The everyday activities of the crystallographer or materials scientist deal with the real physical properties of real objects in the real, three-dimensional space in which we live. Most of these properties can be described, at least approximately, by systems of linear relationships between one set of measurable quantities, “causes,” and another set of measurable quantities, “effects.” We shall find that a useful shorthand for expressing these relationships is the algebra of matrices. To make use of this algebra we need to start, if only to make sure we agree on notation, with definitions of matrices and their fundamental operations.